Volume 15, Issue 2

Shooting skill in the NBA is typically measured by field goal percentage (FG%) – the number of makes out of the total number of shots. Even more advanced metrics like true shooting percentage are calculated by counting each player’s 2-point, 3-point, and free throw makes and misses, ignoring the spatiotemporal data now available (Kubatko et al. 2007). In this paper we aim to better characterize player shooting skill by introducing a new estimator based on post-shot release shot-make probabilities. Via the Rao-Blackwell theorem, we propose a shot-make probability model that conditions probability estimates on shot trajectory information, thereby reducing the variance of the new estimator relative to standard FG%. We obtain shooting information by using optical tracking data to estimate three factors for each shot: entry angle, shot depth, and left-right accuracy. Next we use these factors to model shot-make probabilities for all shots in the 2014–2015 season, and use these probabilities to produce a Rao-Blackwellized FG% estimator (RB-FG%) for each player. We demonstrate that RB-FG% is better than raw FG% at predicting 3-point shooting and true-shooting percentages. Overall, we find that conditioning shot-make probabilities on spatial trajectory information stabilizes inference of FG%, creating the potential to estimate shooting statistics earlier in a season than was previously possible.

Scouting departments at soccer clubs aim to discover players having a positive influence on the outcomes of matches. Since passes are the most frequently occurring on-the-ball actions on the pitch, a natural way to achieve this objective is by identifying players who are effective in setting up chances. Unfortunately, traditional statistics such as number of assists fail to reveal players excelling in this area. To overcome this limitation, this paper introduces a novel metric that measures the players’ involvement in setting up chances by valuing the effectiveness of their passes. Our proposed metric identifies Arsenal player Mesut Özil as the most impactful player in terms of passes during the 2017/2018 season and proposes Ajax player Frenkie de Jong as a suitable replacement for Andrés Iniesta at FC Barcelona.

In a six-day footrace, competitors accumulate as much distance as possible on foot over 144 consecutive hours by circumambulating a loop course. Now an obscure event on the fringe of ultra running and contested by amateurs, six-day races and the associated sport of pedestrianism used to be a lucrative professional athletic endeavor. Indeed, pedestrianism was the most popular spectator sport in America c. 1874–c. 1881. We analyzed data from 277 six-day races spanning 37 years in the post-pedestrianism era (1981–2018). Men outnumber women 3:1 in six-day race participation. The men’s (women’s) six-day world record is 644.2 (549.1) miles and the top 4% achieve 500 (450) miles. Adopting the forecasting model of Godsey (2012), we predict a 53% (21%) probability that the men’s (women’s) world record will be broken within the next decade.

We evaluate the sporting effects of the seeding system reforms in the Champions League, the major football club tournament organized by the Union of European Football Associations (UEFA). Before the 2015–2016 season, the teams were seeded in the group stage by their ratings. Starting from the 2015–2016 season, national champions of the Top-7 associations are seeded in the first pot, whereas other teams are seeded by their rating as before. Taking effect from the season 2018–2019, the team’s rating no longer includes 20% of the rating of the association that the team represents. Using the prediction model, we simulate the whole UEFA season and obtain numerical estimates for competitiveness changes in the UEFA tournaments caused by these seeding reforms. We report only marginal changes in tournament metrics that characterize ability of the tournament to select the best teams and competitive balance. Probability of changes in the UEFA national association ranking does not exceed several percent for any association.

We propose a unsupervised learning framework for automatically labeling events in a basketball game. Our framework uses the the optical player tracking data in the NBA. We first learn the time series of defensive assignments using a novel player and location dependent attraction based model which uses hidden Markov models (HMMs), Gaussian processes, and a “bond breaking” model for changes in defensive assignments. Next, we use the learned defensive assignments as an input to a set of HMMs that automatically detect events such as ball screens, drives and post-ups. We show that our models provide significant improvements over existing benchmarks both on defensive assignments and event detection.

This paper proposes a model that characterizes the degree to which a doubles sport (i.e. two team members) is a weak or a strong link game. The model is applied to the sport of pickleball where interest is focused on the doubles version of the sport. As a byproduct of the analysis, individual player rankings are obtained.